Related papers: The intertwining property for Laguerre processes w…
The masses of the charged fermion and the mixing angles among quarks are observed to be strongly hierarchical, while analogous parameters in the neutrino sector appear to be structure-less or anarchical. We develop a class of unified models…
We consider a certain linear recursive relation with integer parameters and study some of its algebraic and geometric properties, with the purpose of estimating the number of chains of valences in the Farey series.
The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…
A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
We obtain model independent relations among neutrino masses and leptogenesis parameters. We find exact relations that involve the CP asymmetries $\epsilon_{N_\alpha}$, the washout parameters $\tilde m_\alpha$ and $\theta_{\alpha\beta}$, and…
We find the transition kernels for four Markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin-McGregor type kernel. The resulting kernels all inherit the determinantal…
We investigate a model based on hidden $U(1)_X$ gauge symmetry in which neutrino mass is induced at one-loop level by effects of interactions among particles in hidden sector and the Standard Model leptons. Neutrino mass generation is also…
We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…
The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process -- a probability measure on a space of countable point configurations. The kernel is expressed…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
We theoretically introduce a new kind of non-Gaussian state-----Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that…
We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of…
Proposed medium-baseline reactor neutrino experiments offer unprecedented opportunities to probe, at the same time, the mass-mixing parameters which govern $\nu_e$ oscillations both at short wavelength (delta m^2 and theta_{12}) and at long…
Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…